The question is this: How effective will my AR15A3 be with a 4X
scope?

The answer is very, if your scope is dialed in to your ammo. .223 is a good choice. I'd want more like 6-9 power for shots past 100, for extra precision (bad eyes), but 4 will work too. My 20" AR has a 2-7x32mm scope on it (Nikon Prostaff). I'd use soft point ammo though, if not keeping the hide, instead of GI surplus ball ammo, for a quick kill.